In processes of this class (West German Patent Specification No. 3,423,308), some of a series of photocells arranged along the measurement zone at one or several light-collecting bodies are activated, while the others remain passive. The location of the light/dark boundary and consequently the edge of the material web can be determined by polling the signals generated by the photocells. The polling and processing of the signals of the photocells requires highly expensive control means even in a digital scanning mode. The accuracy of determination of the location of the edge is not satisfactory, especially in the case of high-speed material webs performing rapid transverse movements. In addition, measurement over a width zone is expensive if measurement is to be possible over rather great widths.